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ABCA SYNERGY: CHAOS / ORDER.
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ABCAA INFORMATION AND ORDER         1
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This chapter requires some familiarity with the rudiments of physics and
mathematics. It may be skipped by readers lacking this familiarity 
on condition, however, to accept:
1.the physical foundations of informatics as granted and
2.a loose definition of the concept of order.

In the physics, the customary way to express the probability of
a given heat distribution is the ENTROPY E defined by the BOLTZMANN
expression 

(1ada.1):  E = k ln(S) 

where k is the Boltzmanns gas constant and S is the number of 
microscopis states in which the macroscopis state E may be realized. 
The concept of entropy may be generalised by extending the expression 
over all forms of energy. Setting in the generalized expression 
k = 1/ln(2) we get:

(1ada.2): E = ln(S) / ln(2) = log2(S)  (where log2 means log base 2).

1ada.2 allows to express the entropy of the system as the number of 
digits of a binary string capable to address all possible system's 
states. Each digit of this string determines a degree of freedom of 
the system.

Replacing entropy E with information I we may say that the complete 
set of system's states may be addressed with help of I binary bits:

(1ada.3): I = log2(S)

1ada.2 and 1ada.3 express the analogy between the entropy and the 
information.
@
The second law of thermodynamics, the "LAW OF ENTROPY" which may be 
generalised over all practical energetic systems states that any change 
of the system state increases its entropy. In the limit, for the purely
theoretical reversible system, the entropy stays constant. It never
decreases.

Analogically, as result of a communication some of the I bits necessary
to describe the S possible system states may get corrupted in which case
the amount of useful information contained in I decreases. For each 
corrupted bit half of the possible system states S is excluded from the 
information I. This is the customary way of representing the analogy 
between entropy and information: information and entropy are isomorphic 
qualities differing in sign.

ABCAA INFORMATION AND ORDER         2

Another way of presenting the analogy, which we find more appropriate
for the present study is to consider not the information, but the
information carrier as analogous and say that for each corrupted bit 
a new must be added in order to describe all S possible states of 
the system. In this context the analogy becomes strictly isomorphic
and we may refer to I as to the ENTROPY OF INFORMATION, or shortly
ENTROPY, when no misuderstanding about the nature of the involved
system is possible.

Entropy may be considered as the measure of disorder and its inverse 
as measure of order.

Based upon the notion of entropy we define the ORDER of an information
system:

(1ada.4): O = I1 / I

where I is systems entropy in a given situation and
I1 = log2(S) is the minimum possible entropy of the system.
Consequently, the highest possible order is 1. When entropy increases 
order decreases. Its value range is between 1 and 0.

After introduction of the concept of order the law of entropy extended 
over information systems may be called LAW OF DECREASING ORDER and 
formulated: any spontaneous change of a system decreases its order. 
In the limit case of an ideal "reversible system", the order stays 
constant. It never increases.
 
With respect to entropy and order INFORMATICS is analogous to physics.
By virtue of this analogy we shall consider INFORMATICS as a natural
domaine which may be investigated, ordered and processed with help of 
rigorous scientific methods.